{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2009:KXRVDBDYK3YPYN3JXC4U3K2KHF","short_pith_number":"pith:KXRVDBDY","canonical_record":{"source":{"id":"0902.1693","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2009-02-10T16:41:35Z","cross_cats_sorted":[],"title_canon_sha256":"d7bb65f438b0c4fb5d920ce94c1e6976e32334e065607a65f05b6204998d5be5","abstract_canon_sha256":"2af3b4ccb83869bd8e135ba5010c6dea87c75dd5df5ceaa7aab220143b9bc555"},"schema_version":"1.0"},"canonical_sha256":"55e351847856f0fc3769b8b94dab4a3958e29210fa2f5eb16f376fc6f4a7a6e0","source":{"kind":"arxiv","id":"0902.1693","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0902.1693","created_at":"2026-05-18T02:24:56Z"},{"alias_kind":"arxiv_version","alias_value":"0902.1693v4","created_at":"2026-05-18T02:24:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0902.1693","created_at":"2026-05-18T02:24:56Z"},{"alias_kind":"pith_short_12","alias_value":"KXRVDBDYK3YP","created_at":"2026-05-18T12:26:00Z"},{"alias_kind":"pith_short_16","alias_value":"KXRVDBDYK3YPYN3J","created_at":"2026-05-18T12:26:00Z"},{"alias_kind":"pith_short_8","alias_value":"KXRVDBDY","created_at":"2026-05-18T12:26:00Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2009:KXRVDBDYK3YPYN3JXC4U3K2KHF","target":"record","payload":{"canonical_record":{"source":{"id":"0902.1693","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2009-02-10T16:41:35Z","cross_cats_sorted":[],"title_canon_sha256":"d7bb65f438b0c4fb5d920ce94c1e6976e32334e065607a65f05b6204998d5be5","abstract_canon_sha256":"2af3b4ccb83869bd8e135ba5010c6dea87c75dd5df5ceaa7aab220143b9bc555"},"schema_version":"1.0"},"canonical_sha256":"55e351847856f0fc3769b8b94dab4a3958e29210fa2f5eb16f376fc6f4a7a6e0","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:24:56.472547Z","signature_b64":"CgBiDDUrmbYsDYkDqv0K0TsQy3D7U3yTQjZH65cilrH/7eC/VTpETKvJAJ0PQHQxOzs5g3XbcI38o0RnpiCEDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"55e351847856f0fc3769b8b94dab4a3958e29210fa2f5eb16f376fc6f4a7a6e0","last_reissued_at":"2026-05-18T02:24:56.471884Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:24:56.471884Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0902.1693","source_version":4,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:24:56Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"v97Awv8gZoGZQxunnajHg8Qdg+kDIc6hP3JIkFVEcmoQL3RiUBIFOBNfWYp6SeXShacVa0lsBVVsw3B2DDqxDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T08:08:53.473193Z"},"content_sha256":"8f479491bf99c5bbfa1a091ba0e73533241ca544d278fd37b46179b7f40d1ebd","schema_version":"1.0","event_id":"sha256:8f479491bf99c5bbfa1a091ba0e73533241ca544d278fd37b46179b7f40d1ebd"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2009:KXRVDBDYK3YPYN3JXC4U3K2KHF","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Fast Evaluation of Interlace Polynomials on Graphs of Bounded Treewidth","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Christian Hoffmann, Markus Bl\\\"aser","submitted_at":"2009-02-10T16:41:35Z","abstract_excerpt":"We consider the multivariate interlace polynomial introduced by Courcelle (2008), which generalizes several interlace polynomials defined by Arratia, Bollobas, and Sorkin (2004) and by Aigner and van der Holst (2004). We present an algorithm to evaluate the multivariate interlace polynomial of a graph with n vertices given a tree decomposition of the graph of width k. The best previously known result (Courcelle 2008) employs a general logical framework and leads to an algorithm with running time f(k)*n, where f(k) is doubly exponential in k. Analyzing the GF(2)-rank of adjacency matrices in th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0902.1693","kind":"arxiv","version":4},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:24:56Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"XW1JTszkyIK14AtvE2bfevEsRSUQ0epyRIxr73Cno6IWWZVWOdF2satkPggtUUnejf5FBURC2B4KMkNrT51VBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T08:08:53.473550Z"},"content_sha256":"8c978a17007f0fb47d134a7a0e544a724ea10dc87ceb4946951a7ad85febf482","schema_version":"1.0","event_id":"sha256:8c978a17007f0fb47d134a7a0e544a724ea10dc87ceb4946951a7ad85febf482"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/KXRVDBDYK3YPYN3JXC4U3K2KHF/bundle.json","state_url":"https://pith.science/pith/KXRVDBDYK3YPYN3JXC4U3K2KHF/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/KXRVDBDYK3YPYN3JXC4U3K2KHF/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-25T08:08:53Z","links":{"resolver":"https://pith.science/pith/KXRVDBDYK3YPYN3JXC4U3K2KHF","bundle":"https://pith.science/pith/KXRVDBDYK3YPYN3JXC4U3K2KHF/bundle.json","state":"https://pith.science/pith/KXRVDBDYK3YPYN3JXC4U3K2KHF/state.json","well_known_bundle":"https://pith.science/.well-known/pith/KXRVDBDYK3YPYN3JXC4U3K2KHF/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:KXRVDBDYK3YPYN3JXC4U3K2KHF","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"2af3b4ccb83869bd8e135ba5010c6dea87c75dd5df5ceaa7aab220143b9bc555","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2009-02-10T16:41:35Z","title_canon_sha256":"d7bb65f438b0c4fb5d920ce94c1e6976e32334e065607a65f05b6204998d5be5"},"schema_version":"1.0","source":{"id":"0902.1693","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0902.1693","created_at":"2026-05-18T02:24:56Z"},{"alias_kind":"arxiv_version","alias_value":"0902.1693v4","created_at":"2026-05-18T02:24:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0902.1693","created_at":"2026-05-18T02:24:56Z"},{"alias_kind":"pith_short_12","alias_value":"KXRVDBDYK3YP","created_at":"2026-05-18T12:26:00Z"},{"alias_kind":"pith_short_16","alias_value":"KXRVDBDYK3YPYN3J","created_at":"2026-05-18T12:26:00Z"},{"alias_kind":"pith_short_8","alias_value":"KXRVDBDY","created_at":"2026-05-18T12:26:00Z"}],"graph_snapshots":[{"event_id":"sha256:8c978a17007f0fb47d134a7a0e544a724ea10dc87ceb4946951a7ad85febf482","target":"graph","created_at":"2026-05-18T02:24:56Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"We consider the multivariate interlace polynomial introduced by Courcelle (2008), which generalizes several interlace polynomials defined by Arratia, Bollobas, and Sorkin (2004) and by Aigner and van der Holst (2004). We present an algorithm to evaluate the multivariate interlace polynomial of a graph with n vertices given a tree decomposition of the graph of width k. The best previously known result (Courcelle 2008) employs a general logical framework and leads to an algorithm with running time f(k)*n, where f(k) is doubly exponential in k. Analyzing the GF(2)-rank of adjacency matrices in th","authors_text":"Christian Hoffmann, Markus Bl\\\"aser","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2009-02-10T16:41:35Z","title":"Fast Evaluation of Interlace Polynomials on Graphs of Bounded Treewidth"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0902.1693","kind":"arxiv","version":4},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:8f479491bf99c5bbfa1a091ba0e73533241ca544d278fd37b46179b7f40d1ebd","target":"record","created_at":"2026-05-18T02:24:56Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"2af3b4ccb83869bd8e135ba5010c6dea87c75dd5df5ceaa7aab220143b9bc555","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2009-02-10T16:41:35Z","title_canon_sha256":"d7bb65f438b0c4fb5d920ce94c1e6976e32334e065607a65f05b6204998d5be5"},"schema_version":"1.0","source":{"id":"0902.1693","kind":"arxiv","version":4}},"canonical_sha256":"55e351847856f0fc3769b8b94dab4a3958e29210fa2f5eb16f376fc6f4a7a6e0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"55e351847856f0fc3769b8b94dab4a3958e29210fa2f5eb16f376fc6f4a7a6e0","first_computed_at":"2026-05-18T02:24:56.471884Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:24:56.471884Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"CgBiDDUrmbYsDYkDqv0K0TsQy3D7U3yTQjZH65cilrH/7eC/VTpETKvJAJ0PQHQxOzs5g3XbcI38o0RnpiCEDw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:24:56.472547Z","signed_message":"canonical_sha256_bytes"},"source_id":"0902.1693","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8f479491bf99c5bbfa1a091ba0e73533241ca544d278fd37b46179b7f40d1ebd","sha256:8c978a17007f0fb47d134a7a0e544a724ea10dc87ceb4946951a7ad85febf482"],"state_sha256":"9566677671077eb39484f00be008ba1659ec29eec0662f4706cb70ee025b99fc"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"IiXKK2UmGBBSYGk4bFRyUmixcpbzEHcu5R9SAxMIQ31kRTqWorOVP9bSu6h/AUAEURB5pKhXwHVw2pNeiffSAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-25T08:08:53.475428Z","bundle_sha256":"2db06dff17c0a72f99b113930c11f9275fe58e29db523eb64a730e815414fb87"}}